α-cluster structure above doubly closed shells in a generalized density-dependent cluster model

Abstract

An extension of the generalized density-dependent cluster model (GDDCM) is presented to study $\ensuremath{\alpha}$-cluster structure above doubly closed shells. In all cases, the microscopic $\ensuremath{\alpha}$-core potential is numerically constructed in the double-folding model with CDM3Y6 nucleon-nucleon interactions plus proton-proton Coulomb interactions. The properties of intraband $E2$ transitions and $\ensuremath{\alpha}$ decays are calculated by the exact solution of the Schr\"odinger equation with appropriate boundary conditions. It is found that the enhanced $B(E2)$ transition strengths are well reproduced without any effective charge and the calculations of $\ensuremath{\alpha}$-decay properties show good agreement with the available experimental data. This indicates that the GDDCM has universal applicability and equal validity regardless of whether the $\ensuremath{\alpha}$-cluster states are in light or heavy nuclei.